You cannot make Mendeley Desktop stop syncing entirely, but you can stop syncing file attachments to the web library. This can be done by modifying the synchronization settings of your Mendeley Desktop, which you can customise and adjust in the ‘Edit Settings’ pane in the software.

Synchronizing document attachments can be enabled for your entire library, or only for documents in selected collections. Should you wish, you can also choose to disable it altogether.

Ok, thank you for your replay, but what will happen if I exceed 500 MB of personal web space, and I don't want to upgrade and pay for additional web space? Mendeley force me to login every time I collect references and documents, and to sync them.
I could store them first on my computer and then use add files button, and let's say in this case I still don't want to upgrade. What will happen ?

If you exceed your storage space and do not choose to stop syncing file attachments to free up this space, as described above, Mendeley Desktop will stop syncing any new entries to your library to your web library.

So if I understand correctly the files will stay in my Mendeley desktop database (I mean the files that are added with add files button)

They will stay in Mendeley Desktop, but will not be backed up in your online library.